For what value of k are the two lines 2x+ky=3 and x+y=1 (a) parallel? (b) perpendicular?

Question

For what value of k are the two lines 2x+ky=3 and x+y=1 (a) parallel? (b) perpendicular?

Answer 1

Two lines are parallel if they have the same slope and they are perpendicular if their slopes are negative inverses of each other or if the product of their slopes equals -1.

First, you want to write the equation of the lines in slope-intercept form : y = mx + c, where m is the slope and c is the y-intercept. This makes the slopes of the lines more readily apparent.

For the first one: 2x + ky =3, s-i form becomes

ky = 3 - 2x

y = (3/k) - (2x/k)

y = (-2/k)x + (3/k)

So we see that the slope here is (-2/k).

For the second one: x + y = 1, s-i form becomes

y = 1 - x

y = -x + 1

So we see that the slope here is -1.

So for the two lines to be parallel,

(-2/k) must be equal to -1.

-2/k = -1

Multiplying both sides by k, we have

-2 = -k

Multiplying both sides by -1, we have

2 = k. Therefore for both lines to be parallel, k must be equal to 2.

Now for them to be perpendicular,

(-2/k) x ( -1) = -1

2/k = -1

Multiplying both sides by k, we have

2 = -k.

Multiplying both sides by -1, we have

-2 = k.

Therefore for both lines to be perpendicular, k must be equal to -2.

Answer 2

Then,                         ky=-2x+3 &                             y=-x+1

                               slope= -2k                              slope=-1

(a) parallel            when            -2k=-1    so,k=1/2

(b)prependicular    when           -2k(-1)=-1so -2k=1 ===>k=-1/2

Answer 3

Put both lines in y=mx+b form.

2x+ky=3

ky=3-2x

y = (-2/k)x +3/k

y= -x+1

(a) Parallel -------> slopes are equal

-2/k = -1

k=2

(b) Perpendicular ----------> slopes are opposite reciprocals

k/2 = -1

k=-2

Answer 4

Hi,

Writing both lines in slope intercept form

line 1 => 2x + ky = 3 => ky = -2x + 3 => y = (-2/k)x + 3

line 2 => x + y = 1 => y = -x + 1

let slope be represented by m, and the standard form of equation will be => y = mx + c

=> m1 = -2/k

=> m2 = -1

a)Parallel

=> m1 = m2

=> -2/k = -1

=> -2*-1 = k

=> 2 = k

b) perpendicular

=> m1*m2 = -1

=> -2/k * -1 = -1

=> 2/k = -1

=> 2 = -k

=> k = -2

Therefore the lines will be parallel if k = 2 and the lines wil be perpendicular if k = -2.

Hope this helps. Keep smiling. Bye.